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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.15519 |
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| _version_ | 1866911012063543296 |
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| author | Gentili, Giovanni Lejmi, Mehdi |
| author_facet | Gentili, Giovanni Lejmi, Mehdi |
| contents | We prove the openness of the balanced HKT cone within the cone of HKT structures on a compact hypercomplex manifold $(M,I,J,K)$. We also study the Lie algebra of hyperholomorphic vector fields of type (1,0) with respect to $I$, with particular emphasis on the case when there exists a compatible balanced HKT metric. These fields exhibit a strict interplay with the balanced HKT structure, for instance, we prove a harmonicity property for (1,0)-forms dual to hyperholomorphic vector fields. We also show non-existence of hyperholomorphic (1,0)-vector fields on some hypercomplex manifolds admitting a HKT--Einstein metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On balanced HKT manifolds Gentili, Giovanni Lejmi, Mehdi Differential Geometry We prove the openness of the balanced HKT cone within the cone of HKT structures on a compact hypercomplex manifold $(M,I,J,K)$. We also study the Lie algebra of hyperholomorphic vector fields of type (1,0) with respect to $I$, with particular emphasis on the case when there exists a compatible balanced HKT metric. These fields exhibit a strict interplay with the balanced HKT structure, for instance, we prove a harmonicity property for (1,0)-forms dual to hyperholomorphic vector fields. We also show non-existence of hyperholomorphic (1,0)-vector fields on some hypercomplex manifolds admitting a HKT--Einstein metric. |
| title | On balanced HKT manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.15519 |